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C₂×#23486 #6431863

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

5618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(8,9)(11,12)(13,16)(14,22)(15,19)(17,21)(18,24)(20,25)(23,26);(3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,21)(15,20)(17,22)(18,26)(19,25)(23,24);(4,6)(7,9,10,8)(11,13)(12,17)(14,23)(15,20)(16,22)(18,25)(19,26)(21,24);(13,20)(16,25)(17,26)(21,23)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339059);